I like your idea about only four kinds and the ability to leave something off... good for people with allergies (I can't eat carrots, apples, peaches ect.... I know, I know it sounds made up)

I like chicken, cutlets or sliced.

No shredded lettuce please, it is so messy.

For the name how about Which? Since there are only a limited number of choices and they are sandWHICHes? I don't think it is that cutesie but it has potential.